case for momentum investing by aqr (summer 09)

Adam L. Berger, CFA*Vice President, Head of Portfolio Solutions AQR Capital Management, LLC

Ronen IsraelPrincipalAQR Capital Management, LLC

Tobias J. Moskowitz, Ph.D.Fama Family Professor of FinanceBooth School of Business, University of Chicago

S U M M E R 2 0 0 9

The Case for Momentum Investing

Though known to financial academics for many years, momentum is for most investorsthe "undiscovered style,” a valuable tool in building diversified portfolios with above-average returns.

Definition. Momentum is the tendency of investments to exhibit persistence in theirrelative performance. Investments that have performed relatively well, continue to performrelatively well; those that have performed relatively poorly, continue to perform relativelypoorly. Momentum is about much more than buying a handful of hot stocks – it is adisciplined, systematic investing style that applies across asset classes.

Intuition. Momentum is a phenomenon driven by investor behavior: slow reaction tonew information; asymmetric responses to winning and losing investments; and the"bandwagon” effect. Numerous academic and practitioner studies have confirmedmomentum’s existence.

Implications. Virtually all investors can expect higher risk-adjusted returns by addingmomentum to their portfolios. Growth investors will see that momentum delivers muchbetter performance. Value investors will find momentum to be an effective complement.Value-growth investors will want to consider momentum as an alternative to their growthallocation.

This paper introduces a family of investable momentum indices, and in so doing, opensthis powerful strategy to a broad range of investors.

ACKNOWLEDGEMENTS: We would like to thank our AQR colleagues whose extensive contributions, insights and research made thispaper possible: Michele Aghassi, Gregor Andrade, Cliff Asness, Brian Crowell, Andrea Frazzini, Jacques Friedman, Marco Hanig,Sarah Jiang, David Kabiller, Lars Nielsen, Lasse Pedersen, Prasad Ramanan, Sharon Song, London Thomson-Thurm, and Dana Wolf.

*Adam Berger can be reached by email: [email protected]

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PART I – WHAT IS MOMENTUM?

Momentum is the tendency of investments, in everymarket and asset class, to exhibit persistence in theirrelative performance for some period of time.

When applied to stock picking, momentum (like valueor growth) is about relative performance among stocks,and not about overall trends in the market. It workswhether a market is in an upswing or downswing.Momentum can be used to identify securities likely tooutperform, making it a powerful investment tool. It isalso negatively correlated to value investing, making itan effective diversification component. Regardless ofinvestment philosophy, virtually all investors can expectimproved risk-adjusted returns by including momentum.

Historical Evidence

The evidence for momentum is pervasive, supported byalmost two decades of academic research. The first modernstudies were done in the early 1990s,1 and more than 300

published papers have explored momentum since, including150 in the last five years.

EXHIBIT 1 shows the performance of individual U.S.stocks broken into quintiles. Over the next year, thestocks with the best momentum (P5) outperform theones with the worst momentum (P1), both in absoluteterms and relative to the equity market as a whole.

The original momentum studies focused on the periodfrom 1963-1990 in U.S. equities. Subsequent studies havefound momentum in earlier periods2 (as far back as theVictorian age!) and in the out-of-sample period after theoriginal research was published.3 Evidence supportsmomentum in markets outside the U.S.4 and for assetsother than individual stocks, such as industries, bonds,commodities, currencies, and global stock market indices.5

EXHIBIT 2 shows evidence for momentum in a range ofglobal asset classes and markets. Since these are long-shortreturns, they are independent of gains from market exposure.Momentum delivers attractive Sharpe ratios (risk-adjustedreturns) universally.

Exhibit 1: Performance of Stocks with Good and Bad Momentum

Source: AQR Capital Management. Data is based on monthly returns from overlapping portfolios. Momentum is calculated as the past 12-month return excluding themost recent month. *Return in excess of the beta-adjusted CRSP Value Weighted Index.

-10

-5

0

5

10

15

20

P120% of stocks withWorst Momentum

P2 P3 P4 P520% of stocks with

Best Momentum

An

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al R

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rn in

Su

bse

qu

ent

12 M

on

ths

(%)

Average Annual Returns for Portfolios Grouped by Momentum(January 1927 to December 2008)

1 Jegadeesh and Titman (1993), Asness (1994)2 Chabot, Ghysels, and Jagannathan (2009), Grundy and Martin (2001)3 Carhart (1997), Jegadeesh and Titman (2001), Asness, Moskowitz, and Pedersen (2009)4 Europe: Rouwenhorst (1998), Emerging markets: Rouwenhorst (1999), Asia: Chui, Titman, and Wei (2000), Globally in 40 different equity markets: Griffin, Ji, and Martin (2005)5 Asness, Moskowitz, and Pedersen (2009), Industries: Moskowitz and Grinblatt (1999 and 2004), Asness, Porter, Stevens (2000), Countries: Asness, Liew, and Stevens (1997)

Average Return of Each Quintile

Excess Return of Each Quintile*

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6 The past performance of different investments is not a secret. If markets are efficient, this information should be fully incorporated into market prices, and no one should be able to profitby investing in stocks or other investments that have done well recently. The existence of momentum implies that stocks do not (as widely believed) move in a "random walk."7 Many of these explanations are based on the Nobel-prize winning work of Daniel Kahneman and the late Amos Tversky. See, for example, Kahneman and Tversky (1979).8 Research in behavioral finance shows a strong tendency for retail investors and even mutual fund managers to exhibit the disposition effect. See Odean (1998) and Grinblatt and Han(2005) for retail investors and Frazzini (2006) for managers.9 Although these corrections can lead to short-term losses for momentum, our research suggests that equity momentum strategies do not have larger or more frequent drawdowns thanother equity styles (value, growth, and core).

Exhibit 2: Historical Performance of Momentum Across Asset Classes

Sharpe Ratio of a Long-Short

Momentum Strategy

Annualized Return of a Long-Short

Momentum StrategyTime Period

StudiedIn Individual StocksUS 0.7 10.5% 1975-2008

UK 0.6 9.0% 1985-2008

Japan 0.2 3.0% 1985-2008

Continental Europe 1.1 16.5% 1988-2008Stock Markets Equal-Weighted 0.9 13.5% 1988-2008

In Other Asset Classes Bond Markets (Developed) 0.3 4.5% 1975-2008

Currencies (Developed) 0.5 7.5% 1975-2008

Commodities 0.8 12.0% 1975-2008

Equity Indices (Developed) 0.6 9.0% 1975-2008Other Assets Equal-Weighted 0.9 13.5% 1975-2008

Source: Asness, Moskowitz, and Pedersen (2009). The above uses a long-short portfolio to isolate the returns to momentum strategies from their respective directionalmarket returns. Hypothetical long-short back-test where each momentum portfolio is scaled to an estimated 15% annualized volatility based on either AQR or BARRA riskmodels; gross of transaction and financing costs. (Based on our research, adding transaction and financing costs would not have a significant effect on the results shown.)

Second, investors (as human beings) are prone to whatbehavioral economists and experimental psychologistscall the disposition effect. Investors tend to sell winninginvestments prematurely to lock in gains, and hold on tolosing investments too long in the hope of breaking even.The disposition effect creates an artificial headwind:when good news is announced, the price of an asset doesnot immediately rise to its value because of prematureselling. Similarly, when bad news is announced, the pricefalls less because investors are reluctant to sell.8

Third, investors are susceptible to the bandwagon effect(also called over-reaction). Short-term traders may userecent performance as a signal to buy or sell. Longer-terminvestors look to recent performance to confirm theirconvictions. The interaction between these investors cancreate price run-ups or -downs that can persist for manymonths until an eventual correction.9 Notable extremeexamples include the technology bubble of the late 1990sand the energy rally of 2007-2008.

There continues to be a lively debate about the root causesof momentum. (A similar debate is ongoing for valueinvesting as well). What is clear is that the overwhelmingevidence from a range of markets, asset classes, andtime periods supports the argument that momentum isneither a random occurrence nor an effect that disappearsonce the impact of transaction costs is incorporated.

Possible Explanations of Momentum

There are several possible explanations for momentum.One is that momentum’s higher returns are compensationfor some unique risk associated with investments thathave recently outperformed. As of yet, no such risk factorhas been convincingly identified. If it is not compensationfor risk, the existence of momentum seems to challengethe efficient market hypothesis that past price behaviorprovides no information about future behavior.6 In otherwords, momentum is associated with some inefficiency inmarkets, perhaps due to investor behavior. Severalpossible behavioral explanations have been put forth.7

First, investors may be slow to react to new information.Efficient market theory assumes that once new informationis released, it is instantly available to all investors andthat prices immediately adjust to reflect the news. Inpractice, however, different investors (for example, atrader versus a casual investor) receive news from differentsources, and react to news over different time horizonsand in different ways. Also, anchoring and adjustment is abehavioral phenomenon in which individuals update theirviews only partially when faced with new information,slowly accepting its full impact. There is ample evidencesupporting slow-reaction-to-information theories, rangingfrom market response to earnings and dividendannouncements to analysts’ reluctantance to update theirforecasts.

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Time Horizons

Readers may note that momentum may be caused by bothan under-reaction to information (slow assimilation ofnews) and an over-reaction (the bandwagon effect), whichwould perhaps seem to cancel each other out. In fact, theunder-reaction and over-reaction may reinforce oneanother since they typically operate over different timehorizons. Momentum may be initiated by slow reaction toinformation, caused or sustained by behavioral biases likethe disposition effect, then reinforced by the bandwagoneffect over several months. The net result is that momentumwill persist for a period of t ime (6-12 months) beforeultimately leading to reversals as too many investors pileon and prices become detached from fundamentals.

Consistent with this intuition, investments do not exhibitmomentum over just any time horizon. For instance, wecannot say that the stocks that have performed best over

the last five years will do so over the next five years.Indeed, on a five-year horizon we find the opposite effectin the data. Stocks that outperform for a long period oftime will generally become expensive, and expensivestocks tend to under-perform less expensive stocks. Thisis the value effect, and long-run past performance is agood (backwards!) value indicator.10 However, theevidence does show that assets that have performed wellover the last 12 months tend to do better over the next 3-12 months than assets that have performed poorly overthat same period. This is the time horizon in whichmomentum works best.

PART II – INTRODUCING THE AQR MOMENTUM

For an idea with so much support from academic researchand historical evidence, momentum has made surprisinglymodest inroads into investors' portfolios. Contrast thiswith value and size (large cap vs. small cap). There arehundreds of investment funds focused on each of thesestyles, but hardly any based purely on momentum.

One contributing factor is the lack of a momentum index.Academic research on value and size spawned a numberof value and market capitalization indices, such as theS&P and Frank Russell indices. But there are nocomparable equity momentum indices. At the time ofFama and French’s original work on value and size,momentum research was in its infancy.11 Today, over adecade later, momentum is part of virtually every academicmodel and empirical study related to asset pricing.12

We feel momentum is at a point in its history not unlikevalue and growth two decades ago: backed by overwhelmingevidence, but with no real benchmark or index to follow.Now is the time to provide such an index, to givewidespread access to this important investment style.

AQR Momentum Indices: Methodology

AQR has developed an index methodology that capturesmomentum in an intuitive and transparent way, making itaccessible to all investors. For the U.S. market, we havecreated two momentum indices:13

• The AQR Momentum Index (Large Cap and Mid Cap U.S. Equities)

• The AQR Small Cap Momentum Index (Small Cap U.S. Equities)

Determining the Universes. The AQR indices are builtfrom two distinct universes. For the large and mid capU.S. index, we examine the 1,000 largest stocks bymarket capitalization. For the small cap U.S. index, welook at the next 2,000 largest stocks. The universes arescreened using certain liquidity and other criteria.

10 Stocks that have performed relatively well over a 5-year period tend to have poor value and therefore perform relative poorly going forward, as shown by DeBondt and Thaler (1985) andFama and French (1996).11 In their subsequent study on value and size, Fama and French acknowledged that the “main embarrassment of the three-factor model [is] its failure to capture the continuation of short-term returns of Jegadeesh and Titman (1993) and Asness (1994) [later to be known as the momentum effect]” (Fama and French, 1996).12 This includes the recent study of Fama and French (2008), who start by noting that "the anomalous returns associated with... momentum are pervasive." 13 There is also an AQR International Momentum Index (Non-U.S. Equities). This paper focuses on the U.S. indices for ease of exposition, but the international evidence is similar.

INDICES

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Exhibit 3: Performance of the AQR Momentum Indices

Source: AQR Capital Management. Given that the core research on momentum was published in the early 1990s, a large portion of the results shown here are out-of-sample.AQR Momentum Indices are historical indices and not the returns to actual portfolios.

Identifying Momentum. We determine momentum bylooking at the total return of every stock in each universeover the past year.14 As previously discussed, momentumis based on relative rather than absolute performance. Ina sharply falling market, virtually all stocks may have lostmoney in the last year; in this instance, the stocks withthe strongest momentum will be those that fell the least.

Setting the Constituents. Once we have ranked the stocks,we construct the index from the one-third with thestrongest momentum. Within each index, we weight thestocks according to their market capitalization.

Rebalancing. Because momentum is based on recent per-formance, we need to adjust our indices fairly frequently(compared to a value index, for example). Rebalancing ona quarterly basis maintains the momentum characteristicbut does not erode returns through excessive trading.

AQR Momentum Indices: Performance

EXHIBITS 3 and 4 show the performance of the AQRMomentum Index and the AQR Small Cap MomentumIndex relative to a variety of other indices for comparisonpurposes. A few key results stand out:

Performance. The AQR Momentum Indices each out-perform a comparable core index over the period studied.They also outperform other investment styles such asvalue and growth.

Volatility. The AQR Momentum Indices are somewhatmore volatile than the comparable core and value indices,but are similar to growth indices.

Sharpe Ratio. The Sharpe ratios of the AQR MomentumIndices are higher than their comparable core andgrowth indices, and similar to those of value indices. Relativeto a comparable core equity index, the information ratios

14 Note, in calculating the return, we exclude the most recent month to avoid situations in which a stock that has moved sharply in the very short term may be due for a correction. There isevidence across a range of asset classes that sharp, short-term changes in price may be caused by liquidity effects and tend to reverse themselves. Jegadeesh (1990), Lo and MacKinlay(1990), and Lehmann (1990) find strong short-term (one-day to one-month) reversals among stocks. Most academic studies of momentum also exclude the most recent month (see Asness(1994) and Fama and French (1996) for early examples). Excluding the most recent month also lowers the turnover of the index.

AQR Momentum Index

Russell 1000Value Index

Russell 1000Growth Index

Russell 1000Index

Annual Return 13.7% 11.7% 10.6% 11.2%Annualized Volatility 18.6% 14.9% 18.0% 15.7%Sharpe Ratio 0.38 0.35 0.23 0.30

Excess Return over Russell 1000 2.5% 0.5% -0.6%Tracking Error to Russell 1000 8.1% 5.1% 4.9%Information Ratio 0.30 0.10 -0.13Correlation to Momentum Index 1.00 -0.50 0.43

Estimated Transactions Costs 0.7%

January 1980 - April 2009

AQR Small CapMomentum Index

Russell 2000Value Index

Russell 2000Growth Index

Russell 2000Index

Annual Return 15.4% 12.8% 9.6% 11.2%Annualized Volatility 22.2% 17.1% 23.0% 19.5%Sharpe Ratio 0.40 0.36 0.13 0.24

Excess Return over Russell 2000 4.2% 1.6% -1.6%Tracking Error to Russell 2000 7.0% 6.2% 5.7%Information Ratio 0.60 0.25 -0.29Correlation to Momentum Index 1.00 -0.58 0.51

Estimated Transactions Costs 1.5%

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-20%

-10%

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1980

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2008

Correlation: 0.4

Annual Excess Returns of AQR Momentum Index and Russell 1000 Growth Index

-20%

-10%

0%

10%

20%

30%

1980

1981

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1989

1990

1991

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2007

2008

Source: AQR Capital Management. January 1980 to December 2008. Returns are excess to Russell 1000 Index. AQR Momentum Index is a historical index and does notrepresent the returns to actual portfolios.

Correlation: -0.5

Annual Excess Returns of AQR Momentum Index and Russell 1000 Value Index

of the AQR Momentum Indices are higher than those ofgrowth and value indices.

Correlation. The excess returns of the AQR MomentumIndices (over a core equity index) are positively correlatedto the excess returns of a comparable growth index, andnegatively correlated to the excess returns of a comparablevalue index (see EXHIBIT 4). As we will show in the nextsection, these correlations make momentum a better alter-native to growth and an attractive complement to value.

Transaction Costs. In EXHIBIT 3, neither the AQRMomentum Indices nor the comparison indices reflectany transaction costs. However, transaction costs are

important, and we have included an estimate of thesecosts for the AQR Momentum Indices. The costs are notinsignificant (0.7% annually for large cap and 1.5% forsmall cap), but they are not high enough to materiallychange the attractiveness of momentum, both in absoluteterms and relative to value and growth.

Backtests do have inherent limitations. However, basedon the historical evidence from academia, the wealth ofout-of-sample evidence from other time periods and assetclasses, along with AQR's experience with momentum-based strategies for over a decade, we are confident thatour indices capture the characteristics of momentuminvesting.

AQR Momentum Index

Russell 1000 Growth Index

Exhibit 4: Comparing Momentum to Growth and Value

AQR Momentum Index

Russell 1000 Value Index

715 The historical underperformance of growth investing is documented extensively by Fama and French (1992) and Lakonishok, Shleifer, and Vishny (1994). In our analysis, we use theFrank Russell U.S. style indices to illustrate the performance of growth (and value).

Exhibit 5: Adding Momentum to a Growth-Focused Portfolio

90%

10%

Source: AQR Capital Management. January 1980 to April 2009. We assume a 90/10 split between large cap and small cap. The returns shown are gross of transactioncosts. Based on our research, adding transaction costs for the various strategies would not have a significant effect on the improvements shown.

Growth-FocusedPortfolio

PartiallyReplacing Growthwith Momentum

Fully Replacing Growthwith Momentum

5%

45% 45%

5% 10%

90%

Russell 1000 Growth

Russell 2000 Growth

AQR Momentum

AQR Small Cap Momentum

PART III – INVESTING IN MOMENTUM

Many investors already think about style exposures aspart of the asset allocation process (i.e., large cap vs.small cap, value vs. growth). Momentum is a powerfulstyle that can improve any asset allocation strategy. Itoffers better returns than growth and is a better complementto value. For a typical investor, shifting assets fromgrowth equity to momentum equity results in a moreefficient portfolio with a higher expected return.

Momentum vs. Growth

Growth equity is a large part of many portfolios. Growthinvestors typically seek to reap gains from owning sharesof successful companies that are expanding theirbusinesses and profits. However, at the index level, the

fact is that growth equity has underperformed core equityinvesting.15 This is not to say that some active growthmanagers may not be able to outperform the overall marketbenchmark, but the historical performance of growthindices suggests that they do start with a handicap.

The evidence shows that growth style investors would dobetter to shift some or all of their exposure to momentumstrategies. Since 1980, the AQR Momentum Index hasoutperformed the Russell 1000 Growth Index by an averageof 3% per year. Over this period growth and momentum arealso strongly positively correlated (shown in EXHIBITS 3and 4), implying that momentum may be an appealing sub-stitute for growth. EXHIBIT 5 shows the impact of movingfrom a growth-focused portfolio to one built aroundmomentum. The momentum portfolio has better performance,both in absolute terms and relative to a core index.

Portfolio Return 10.5% 12.2% 13.8%Volatility 18.2% 18.1% 18.7%Sharpe Ratio 0.22 0.31 0.39

Excess Return over Russell 3000 -0.7% 1.0% 2.7%Tracking Error to Russell 3000 4.9% 5.5% 7.9%Information Ratio -0.14 0.18 0.34

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Exhibit 6: Adding Momentum to a Value-Focused Portfolio

10%

90%


Adding SomeMomentum

50/50Momentum & Value

Portfolio

22.5%

67.5%7.5%

2.5%

5%

45% 45%

5%

Russell 1000 ValueRussell 2000 ValueAQR MomentumAQR Small Cap Momentum

Value-FocusedPortfolio

Momentum vs. Value

While value stocks have historically outperformed growthstocks, focusing exclusively on value also has its drawbacks.A value-focused strategy has substantial tracking errorrelative to core equity benchmarks. Value periodicallyfalls out of favor and the returns suffer dramatic reversals,16

costing investors in the short term and often leading themto give up on value strategies at exactly the wrong time.Value investors who make poor timing decisions may endup faring worse than investors who hold core indexportfolios.

16 For example, for the two years ending in March 2000, the Russell 1000 Value Index underperformed the core Russell 1000 by 30%. 17 The negative correlation between value and momentum has an intuitive explanation. Stocks with good momentum tend to have risen in price and offer less value, while stocks with goodvalue have often fallen in price and have poor momentum.


Excess Return over Russell 3000 0.7% 1.2% 1.7%Tracking Error to Russell 3000 5.1% 3.3% 3.4%Information Ratio 0.13 0.36 0.49

Like value, momentum has historically outperformed coreequity benchmarks. Moreover, value and momentum arenegatively correlated17 (shown in EXHIBITS 3 and 4),which offers a big advantage. Investors in value may seelosing streaks, as may investors in momentum. Butinvestors who combine value and momentum are betterprotected, since the strategies rarely move together. Thisis the true power of diversification.

EXHIBIT 6 compares the historical performance of avalue-focused portfolio to two different value-plus-momentum portfolios. Adding momentum to a valueportfolio leads to higher returns with less tracking errorrelative to a core equity portfolio.


Excess Return over Russell 3000 — 0.8% 1.7%Tracking Error to Russell 3000 — 1.7% 3.4%Information Ratio — 0.51 0.49

For more information on the AQR Momentum Indices,please visit www.aqrindex.com.

AQR Index (Ticker Symbol)AQR Momentum Index (AQRMOMLC)AQR Small Cap Momentum Index (AQRMOMSC)AQR International Momentum Index (AQRMOMIL)

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Exhibit 7: Adding Momentum to a Value & Growth Portfolio

45%

5%

5%

45%


Growth & Value(or Core)Portfolio

PartiallyReplacing Growthwith Momentum

Fully Replacing Growthwith Momentum

(50/50 Momentum & Value Portfolio)

22.5%

45%2.5%

5%

22.5%

2.5%

45%

5%

5%

45%

Russell 1000 Value

Russell 2000 Value

Russell 1000 Growth

Russell 2000 Growth

AQR Momentum

AQR Small Cap Momentum

Momentum in a Portfolio

Portfolios rarely consist exclusively of value stocks orgrowth stocks. Most investors allocate to both styles, andoften include active management. Value is a naturalallocation because of its attractive return characteristics.Growth, on the other hand, has historically underper-formed a core equity index. We believe that value-growthindex investors should consider substituting momentumfor some – arguably all – of their growth index exposure.An assessment of this substitution is shown in EXHIBIT 7.The improvement in both the Sharpe ratio and informationratio is substantial when substituting momentum forgrowth in the portfolio.

Other investors focus on core equity, often employing apassive approach through the S&P 500, Russell 1000, orMSCI World indices. Because combining a value indexand a growth index by definition results in a core indexportfolio, EXHIBIT 7 also illustrates the advantage of shiftingfrom a core index portfolio to a value-plus-momentumindexed portfolio. The debate about the virtues of indexingversus active management goes beyond the scope of thispaper, but readers should note that momentum indices canbe viewed as a low-cost “active” strategy relative to agrowth index.

Conclusion

Momentum is a powerful investment style, nearlyunmatched in its predictive strength and robustness.Today, momentum is at a point similar to that of valuetwo decades ago: fully adopted by the academic community,long used by leading institutional investors, but withoutan investable index and therefore largely unavailable tothe broader investment community.

The introduction of the AQR Momentum Indices representsa pivotal development in momentum’s emergence as awidely accepted investment strategy. Momentum willenable all investors to enhance their portfolio diversificationand increase their expected risk-adjusted returns.

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D ISCLAIMER:

Copyright © AQR Capital Management, LLC 2009. This material is proprietary and may not be reproduced, transferred or distributed in any formwithout prior written permission from AQR Capital Management, LLC (“AQR”).

You cannot invest directly in the AQR Momentum Indices. Index performance does not represent actual fund or portfolio performance. A fund orportfolio may differ significantly from the securities included in the Indices. Index performance assumes reinvestment of dividends, but does notreflect any management fees, transaction costs or other expenses that would be incurred by a portfolio or fund, or brokerage commissions ontransactions in fund shares. Such fees, expenses and commissions would reduce returns.

Past performance does not guarantee future results. No representation is being made that any investment will achieve performance similar to thoseshown. All information is provided strictly for educational and illustrative purposes only. The information provided is not intended for tradingpurposes, and should not be considered investment advice.

Performance information presented herein for the AQR Momentum Indices (“Indices”) are based on hypothetical back tested data for the specifiedtime period(s) shown and were not calculated in real time by an independent calculation agent. The hypothetical back tests for the AQR MomentumIndices utilize certain historical data provided by third parties, which are used by permission, and which are not warranted or represented to becomplete or accurate. A back test is an indication of how an index would have performed in the past if it had existed. Hypothetical back testedperformance has inherent limitations.

AQR, its affiliates and their independent providers are not liable for any informational errors, incompleteness, or delays, or for any actions taken inreliance on information contained herein. AQR reserves the right at any time and without notice, to change, amend or cease publication of the Indices.AQR assumes no responsibility for the accuracy or completeness of the above data and disclaims all express or implied warranties in connectiontherewith.

AQR Momentum Index, AQR Small Cap Momentum Index, and AQR International Momentum Index (the “Indices”) are the exclusive property ofAQR Capital Management, LLC (“AQR”), which has contracted with Standard & Poor’s Financial Services LLC (“S&P”) to maintain and calculate theIndices. Standard & Poor’s® and S&P® are registered trademarks of S&P. “Calculated by S&P Custom Indices” and its related stylized mark(s) areservice marks of S&P and have been licensed for use by AQR. S&P and its affiliates shall have no liability for any errors or omissions in calculatingthe Index.

Performance information for the AQR Indices prior to June 30, 2009 is based on hypothetical back tested monthly data and was not calculated by anindependent calculation agent. The hypothetical back tests for the AQR Momentum Indices utilize certain historical data provided by third parties,which are used by permission, and which are not warranted or represented to be complete or accurate. A back test is an indication of how an indexwould have performed in the past if it had existed. Hypothetical back tested performance has inherent limitations. Starting July 1, 2009, the AQRIndices are calculated daily by S&P as calculation agent.

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case for momentum investing by aqr (summer 09)

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